The GZK Feature in our Neighborhood of the Universe

We calculate numerically the spectrum of ultra-high energy cosmic rays on Earth assuming that their sources are distributed in space like the observed galaxies. We use the CfA2 and the PSCz galaxy redshift surveys to model the local galaxy distribution, properly taking into account the galaxy selection functions for each survey. When the survey selection effects are included, we find that the local overdensity is only a factor of two, an order of magnitude less than used in some earlier studies. An overdensity of two is not enough to bridge the gap between the predicted number of events above \(10^{20}\) eV and the measured flux at these highest energies. This conclusion is particularly strong for soft injection spectra (\(\propto E^{-3}\)) where the observed number of events is 6 \(\sigma\) higher than the expected one. However, if the injection spectrum is hard (\(\propto E^{-2}\)), the small local overdensity helps bring the present data within 2\(\sigma\) of the low number of events predicted above \(10^{20}\) eV. In this case, the Greisen-Zatzepin-Kuzmin cutoff is not a {\it cutoff} but rather a {\it feature} in the cosmic ray spectrum.